By the traditional approach to the Brownian dynamics simulations of intrachain reactions of polymers, the initial chain conformation is sampled from the equilibrium distribution. A dynamic trajectory is carried out until a "collision" of the reactive groups takes place, i.e., the distance between their centers becomes less that a certain reaction radius. The average length of the trajectory is equal to the mean time tau(F) of a diffusion-controlled reaction. In this work we propose another computational scheme. The trajectory begins at the instant of collision and is carried out until the chain is relaxed. The length of the trajectory has the order of the relaxation time tau(rel) of the distance between the reactive groups. For polymer systems with tau(rel)much greater than tau(F), this scheme allows the computation of tau(F) with considerable gain in computational time. Using the present approach, we calculated the mean time of DNA cyclization for the molecule length in the range from 50 to 500 nm. (C) 2004 American Institute of Physics.